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version 1.7, 2002/06/28 13:03:41 version 1.8, 2002/07/09 23:38:57
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 ]><archimedes>      <info>        <author>Newton, Isaac</author>        <title>Philosophiae Naturalis Principia Mathmatica</title>        <date>1713</date>        <place>Cambridge</place>     <editor></editor>                <publisher></publisher>        <translator></translator>        <lang>la</lang>              <chunk unit="page*">page</chunk>        <locator>0000000039</locator>      </info>      <text>          <front>          </front>          <body>            <chap>        <pb/><p type="main"> ]><archimedes>      <info>        <author>Newton, Isaac</author>        <title>Philosophiae Naturalis Principia Mathmatica</title>        <date>1713</date>        
  
  
  <place>Cambridge</place>        <editor></editor>                <publisher></publisher>        <translator></translator>        <lang>la</lang>              <chunk unit="page*">page</chunk>        <locator>0000000039</locator>      </info>      <text>          <front>          </front>          <body>            <chap>        <pb/><p type="main">
  
 <s><emph type="center"/>PHILOSOPHI&AElig; <lb/>NATURALIS <lb/>PRINCIPIA <lb/>MATHEMATICA.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/>PHILOSOPHI&AElig; <lb/>NATURALIS <lb/>PRINCIPIA <lb/>MATHEMATICA.<emph.end type="center"/></s></p><p type="main">
  
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 <s><emph type="italics"/>Moveatur corpus in Circulo<emph.end type="italics"/> PQA: <emph type="italics"/>ad hunc effectum requiritur Lex <lb/>vis centripet&aelig; tendentis ad punctum adeo longinquum<emph.end type="italics"/> S, <emph type="italics"/>ut line&aelig; <lb/>omnes<emph.end type="italics"/> PS, RS <emph type="italics"/>ad id duct&aelig;, pro parallelis haberi po&longs;&longs;int.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Moveatur corpus in Circulo<emph.end type="italics"/> PQA: <emph type="italics"/>ad hunc effectum requiritur Lex <lb/>vis centripet&aelig; tendentis ad punctum adeo longinquum<emph.end type="italics"/> S, <emph type="italics"/>ut line&aelig; <lb/>omnes<emph.end type="italics"/> PS, RS <emph type="italics"/>ad id duct&aelig;, pro parallelis haberi po&longs;&longs;int.<emph.end type="italics"/></s></p><p type="main">
  
 <s>A Circuli centro <emph type="italics"/>C<emph.end type="italics"/> agatur &longs;emidiameter <emph type="italics"/>CA<emph.end type="italics"/> parallelas i&longs;tas <lb/>perpendiculariter &longs;ecans in <emph type="italics"/>M<emph.end type="italics"/> &amp; <lb/><figure id="fig16"></figure><lb/><emph type="italics"/>N,<emph.end type="italics"/> &amp; jungatur <emph type="italics"/>CP.<emph.end type="italics"/> Ob &longs;imilia <lb/>triangula <emph type="italics"/>CPM, PZT<emph.end type="italics"/> &amp; <emph type="italics"/>RZQ<emph.end type="italics"/><lb/>e&longs;t <emph type="italics"/>CPq<emph.end type="italics"/> ad <emph type="italics"/>PMq<emph.end type="italics"/> ut <emph type="italics"/>PRq<emph.end type="italics"/> ad <lb/><emph type="italics"/>QTq<emph.end type="italics"/> &amp; ex natura Circuli <emph type="italics"/>PRq<emph.end type="italics"/><lb/>&aelig;quale e&longs;t rectangulo <emph type="italics"/>QRX&radic;RN+QN<emph.end type="italics"/> &amp;c. <lb/>&longs;ive coeuntibus punctis <emph type="italics"/>P, Q<emph.end type="italics"/> rect&shy;<lb/>angulo <emph type="italics"/>QRX2PM.<emph.end type="italics"/> Ergo e&longs;t <lb/><emph type="italics"/>CPq<emph.end type="italics"/> ad <emph type="italics"/>PM quad.<emph.end type="italics"/> ut <emph type="italics"/>QRX2PM<emph.end type="italics"/><lb/>ad <emph type="italics"/>QT quad.<emph.end type="italics"/> adeoque (<emph type="italics"/>QT quad./QR<emph.end type="italics"/>) <lb/>&aelig;quale (2<emph type="italics"/>PM cub./CP quad.<emph.end type="italics"/>), &amp; (<emph type="italics"/>QT quad.XSP quad./QR<emph.end type="italics"/>) &aelig;quale (2<emph type="italics"/>PM cub.XSP qu./CP quad.<emph.end type="italics"/>) <lb/>E&longs;t ergo (per Corol. </s> <s>A Circuli centro <emph type="italics"/>C<emph.end type="italics"/> agatur &longs;emidiameter <emph type="italics"/>CA<emph.end type="italics"/> parallelas i&longs;tas <lb/>perpendiculariter &longs;ecans in <emph type="italics"/>M<emph.end type="italics"/> &amp; <lb/><figure id="fig16"></figure><lb/><emph type="italics"/>N,<emph.end type="italics"/> &amp; jungatur <emph type="italics"/>CP.<emph.end type="italics"/> Ob &longs;imilia <lb/>triangula <emph type="italics"/>CPM, PZT<emph.end type="italics"/> &amp; <emph type="italics"/>RZQ<emph.end type="italics"/><lb/>e&longs;t <emph type="italics"/>CPq<emph.end type="italics"/> ad <emph type="italics"/>PMq<emph.end type="italics"/> ut <emph type="italics"/>PRq<emph.end type="italics"/> ad <lb/><emph type="italics"/>QTq<emph.end type="italics"/> &amp; ex natura Circuli <emph type="italics"/>PRq<emph.end type="italics"/><lb/>&aelig;quale e&longs;t rectangulo <emph type="italics"/>QRX&radic;RN+QN<emph.end type="italics"/> &amp;c. <lb/></s>
  
  <s>&longs;ive coeuntibus punctis <emph type="italics"/>P, Q<emph.end type="italics"/> rect&shy;<lb/>angulo <emph type="italics"/>QRX2PM.<emph.end type="italics"/> Ergo e&longs;t <lb/><emph type="italics"/>CPq<emph.end type="italics"/> ad <emph type="italics"/>PM quad.<emph.end type="italics"/> ut <emph type="italics"/>QRX2PM<emph.end type="italics"/><lb/>ad <emph type="italics"/>QT quad.<emph.end type="italics"/> adeoque (<emph type="italics"/>QT quad./QR<emph.end type="italics"/>) <lb/>&aelig;quale (2<emph type="italics"/>PM cub./CP quad.<emph.end type="italics"/>), &amp; (<emph type="italics"/>QT quad.XSP quad./QR<emph.end type="italics"/>) &aelig;quale (2<emph type="italics"/>PM cub.XSP qu./CP quad.<emph.end type="italics"/>) <lb/>E&longs;t ergo (per Corol. </s>
  
 <s>1 &amp; 5 Prop. </s> <s>1 &amp; 5 Prop. </s>
  
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 <s><margin.target id="note148"></margin.target>DE MOTU <lb/>CORPORUM</s></p><p type="main"> <s><margin.target id="note148"></margin.target>DE MOTU <lb/>CORPORUM</s></p><p type="main">
  
 <s><emph type="italics"/>Corol.<emph.end type="italics"/> 1. Hinc &longs;i &longs;ingula Sy&longs;tematis corpora <emph type="italics"/>A, B, C, D,<emph.end type="italics"/> &amp;c. <lb/>&longs;eor&longs;im &longs;pectata trahant c&aelig;tera omnia viribus acceleratricibus qu&aelig; <lb/>&longs;unt reciproce ut quadrata di&longs;tantiarum a trahente; erunt corpo&shy;<lb/>rum illorum omnium vires ab&longs;olut&aelig; ad invicem ut &longs;unt ip&longs;a cor&shy;<lb/>pora. </s></p><p type="main"> <s><emph type="italics"/>Corol.<emph.end type="italics"/> 1. Hinc &longs;i &longs;ingula Sy&longs;tematis corpora <emph type="italics"/>A, B, C, D,<emph.end type="italics"/> &amp;c. <lb/></s>
  
  <s>&longs;eor&longs;im &longs;pectata trahant c&aelig;tera omnia viribus acceleratricibus qu&aelig; <lb/>&longs;unt reciproce ut quadrata di&longs;tantiarum a trahente; erunt corpo&shy;<lb/>rum illorum omnium vires ab&longs;olut&aelig; ad invicem ut &longs;unt ip&longs;a cor&shy;<lb/>pora. </s></p><p type="main">
  
 <s><emph type="italics"/>Corol.<emph.end type="italics"/> 2. Eodem argumento, &longs;i &longs;ingula Sy&longs;tematis corpora <lb/><emph type="italics"/>A, B, C, D,<emph.end type="italics"/> &amp;c. </s> <s><emph type="italics"/>Corol.<emph.end type="italics"/> 2. Eodem argumento, &longs;i &longs;ingula Sy&longs;tematis corpora <lb/><emph type="italics"/>A, B, C, D,<emph.end type="italics"/> &amp;c. </s>
  
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 <s>product&aelig; occurrant Hyperbol&aelig; <lb/>in <emph type="italics"/>q, r, s, t,<emph.end type="italics"/> &amp;c. </s> <s>product&aelig; occurrant Hyperbol&aelig; <lb/>in <emph type="italics"/>q, r, s, t,<emph.end type="italics"/> &amp;c. </s>
  
 <s>erunt are&aelig; <emph type="italics"/>ABqK, KqrL, LrsM, MstN,<emph.end type="italics"/> &amp;c. <lb/>&aelig;quales, adeoque tum temporibus tum viribus gravitatis &longs;emper <lb/>&aelig;qualibus analog&aelig;. </s> <s>erunt are&aelig; <emph type="italics"/>ABqK, KqrL, LrsM, MstN,<emph.end type="italics"/> &amp;c. <lb/></s>
  
  <s>&aelig;quales, adeoque tum temporibus tum viribus gravitatis &longs;emper <lb/>&aelig;qualibus analog&aelig;. </s>
  
 <s>E&longs;t autem area <emph type="italics"/>ABqK<emph.end type="italics"/> (per Corol. </s> <s>E&longs;t autem area <emph type="italics"/>ABqK<emph.end type="italics"/> (per Corol. </s>
  
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 <s>I) ad aream <emph type="italics"/>Bkq<emph.end type="italics"/> ut <emph type="italics"/>Kq<emph.end type="italics"/> ad 1/2 <emph type="italics"/>kq<emph.end type="italics"/> &longs;eu <emph type="italics"/>AC<emph.end type="italics"/> ad 1/2 <emph type="italics"/>AK,<emph.end type="italics"/><lb/>hoc e&longs;t, ut vis gravitatis ad re&longs;i&longs;tentiam in medio temporis primi. </s> <s>I) ad aream <emph type="italics"/>Bkq<emph.end type="italics"/> ut <emph type="italics"/>Kq<emph.end type="italics"/> ad 1/2 <emph type="italics"/>kq<emph.end type="italics"/> &longs;eu <emph type="italics"/>AC<emph.end type="italics"/> ad 1/2 <emph type="italics"/>AK,<emph.end type="italics"/><lb/>hoc e&longs;t, ut vis gravitatis ad re&longs;i&longs;tentiam in medio temporis primi. </s>
  
 <s><lb/>Et &longs;imili argumento are&aelig; <lb/><figure id="fig135"></figure><lb/><emph type="italics"/>qKLr, rLMs, sMNt,<emph.end type="italics"/> &amp;c. <lb/>&longs;unt ad areas <emph type="italics"/>qklr, rlms, <lb/>smnt,<emph.end type="italics"/> &amp;c. </s> <s><lb/>Et &longs;imili argumento are&aelig; <lb/><figure id="fig135"></figure><lb/><emph type="italics"/>qKLr, rLMs, sMNt,<emph.end type="italics"/> &amp;c. <lb/></s>
  
  <s>&longs;unt ad areas <emph type="italics"/>qklr, rlms, <lb/>smnt,<emph.end type="italics"/> &amp;c. </s>
  
 <s>ut vires gravi&shy;<lb/>tatis ad re&longs;i&longs;tentias in me&shy;<lb/>dio temporis &longs;ecundi, ter&shy;<lb/>tii, quarti, &amp;c. </s> <s>ut vires gravi&shy;<lb/>tatis ad re&longs;i&longs;tentias in me&shy;<lb/>dio temporis &longs;ecundi, ter&shy;<lb/>tii, quarti, &amp;c. </s>
  
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 <s>erunt in progre&longs;&longs;ione Geo&shy;<lb/>metrica. <emph type="italics"/>q.E.D.<emph.end type="italics"/> Et &longs;imili argumento, in a&longs;cen&longs;u corporis, &longs;u&shy;<lb/>mendo, ad contrariam partem puncti <emph type="italics"/>A,<emph.end type="italics"/> &aelig;quales areas <emph type="italics"/>ABmi, <lb/>imnk, knol,<emph.end type="italics"/> &amp;c. </s> <s>erunt in progre&longs;&longs;ione Geo&shy;<lb/>metrica. <emph type="italics"/>q.E.D.<emph.end type="italics"/> Et &longs;imili argumento, in a&longs;cen&longs;u corporis, &longs;u&shy;<lb/>mendo, ad contrariam partem puncti <emph type="italics"/>A,<emph.end type="italics"/> &aelig;quales areas <emph type="italics"/>ABmi, <lb/>imnk, knol,<emph.end type="italics"/> &amp;c. </s>
  
 <s>con&longs;tabit quod vires ab&longs;olut&aelig; <emph type="italics"/>AC, iC, kC, lC,<emph.end type="italics"/> &amp;c. <lb/>&longs;unt continue proportionales. </s> <s>con&longs;tabit quod vires ab&longs;olut&aelig; <emph type="italics"/>AC, iC, kC, lC,<emph.end type="italics"/> &amp;c. <lb/></s>
  
  <s>&longs;unt continue proportionales. </s>
  
 <s>Ideoque &longs;i &longs;patia omnia in a&longs;cen&longs;u &amp; <lb/>de&longs;cen&longs;u capiantur &aelig;qualia; omnes vires ab&longs;olut&aelig; <emph type="italics"/>lC, kC, iC, AC, <lb/>IC, KC, LC,<emph.end type="italics"/> &amp;c. </s> <s>Ideoque &longs;i &longs;patia omnia in a&longs;cen&longs;u &amp; <lb/>de&longs;cen&longs;u capiantur &aelig;qualia; omnes vires ab&longs;olut&aelig; <emph type="italics"/>lC, kC, iC, AC, <lb/>IC, KC, LC,<emph.end type="italics"/> &amp;c. </s>
  
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 <s><emph type="italics"/>Corol.<emph.end type="italics"/> Igitur &longs;i longitudo aliqua V &longs;umatur in ea ratione ad du&shy;<lb/>plum longitudinis M, qu&aelig; oritur applicando aream <emph type="italics"/>DET<emph.end type="italics"/> ad <emph type="italics"/>BD,<emph.end type="italics"/><lb/>quam habet linea <emph type="italics"/>DA<emph.end type="italics"/> ad lineam <emph type="italics"/>DE<emph.end type="italics"/>; &longs;patium quod corpus a&longs;cen&shy;<lb/>&longs;u vel de&longs;cen&longs;u toto in Medio re&longs;i&longs;tente de&longs;cribit, erit ad &longs;patium <lb/>quod in Medio non re&longs;i&longs;tente eodem tempore de&longs;cribere po&longs;&longs;et, <lb/>ut arearum illarum differentia ad (<emph type="italics"/>BD<emph.end type="italics"/>XV<emph type="sup"/>2<emph.end type="sup"/>/4<emph type="italics"/>AB<emph.end type="italics"/>), ideoque ex dato tem&shy;<lb/>pore datur. </s> <s><emph type="italics"/>Corol.<emph.end type="italics"/> Igitur &longs;i longitudo aliqua V &longs;umatur in ea ratione ad du&shy;<lb/>plum longitudinis M, qu&aelig; oritur applicando aream <emph type="italics"/>DET<emph.end type="italics"/> ad <emph type="italics"/>BD,<emph.end type="italics"/><lb/>quam habet linea <emph type="italics"/>DA<emph.end type="italics"/> ad lineam <emph type="italics"/>DE<emph.end type="italics"/>; &longs;patium quod corpus a&longs;cen&shy;<lb/>&longs;u vel de&longs;cen&longs;u toto in Medio re&longs;i&longs;tente de&longs;cribit, erit ad &longs;patium <lb/>quod in Medio non re&longs;i&longs;tente eodem tempore de&longs;cribere po&longs;&longs;et, <lb/>ut arearum illarum differentia ad (<emph type="italics"/>BD<emph.end type="italics"/>XV<emph type="sup"/>2<emph.end type="sup"/>/4<emph type="italics"/>AB<emph.end type="italics"/>), ideoque ex dato tem&shy;<lb/>pore datur. </s>
  
 <s>Nam &longs;patium in Medio non re&longs;i&longs;tente e&longs;t in dupli&shy;<lb/>cata ratione temporis, &longs;ive ut V<emph type="sup"/>2<emph.end type="sup"/>, &amp; ob datas <emph type="italics"/>BD<emph.end type="italics"/> &amp; <emph type="italics"/>AB,<emph.end type="italics"/> ut <pb pagenum="252"/><arrow.to.target n="note228"></arrow.to.target><lb/>(<emph type="italics"/>BD<emph.end type="italics"/>XV<emph type="sup"/>2<emph.end type="sup"/>/4<emph type="italics"/>AB<emph.end type="italics"/>). Momentum hujus are&aelig; &longs;ive huic &aelig;qualis (<emph type="italics"/>DAqXBD<emph.end type="italics"/>XM<emph type="sup"/>2<emph.end type="sup"/>/<emph type="italics"/>DEqXAB<emph.end type="italics"/>) <lb/>e&longs;t ad momentum differenti&aelig; arearum <emph type="italics"/>DET<emph.end type="italics"/> &amp; <emph type="italics"/>AbNK,<emph.end type="italics"/> ut <lb/>(<emph type="italics"/>DAqXBD<emph.end type="italics"/>X2MX<emph type="italics"/>m<emph.end type="italics"/>/<emph type="italics"/>DEqXAB<emph.end type="italics"/>) ad (<emph type="italics"/>APXBDXm/AB<emph.end type="italics"/>), hoc e&longs;t, ut (<emph type="italics"/>DAqXBD<emph.end type="italics"/>XM/<emph type="italics"/>DEq<emph.end type="italics"/>) <lb/>ad 1/2<emph type="italics"/>BDXAP,<emph.end type="italics"/> &longs;ive ut (<emph type="italics"/>DAq/DEq<emph.end type="italics"/>) in <emph type="italics"/>DET<emph.end type="italics"/> ad <emph type="italics"/>DAP<emph.end type="italics"/>; adeoque ubi <lb/>are&aelig; <emph type="italics"/>DET<emph.end type="italics"/> &amp; <emph type="italics"/>DAP<emph.end type="italics"/> quam minim&aelig; &longs;unt, in ratione &aelig;qualitatis. <lb/>&AElig;qualis igitur e&longs;t area quam minima (<emph type="italics"/>BD<emph.end type="italics"/>XV<emph type="sup"/>2<emph.end type="sup"/>/4<emph type="italics"/>AB<emph.end type="italics"/>) differenti&aelig; quam <lb/>minim&aelig; arearum <emph type="italics"/>DET<emph.end type="italics"/> &amp; <emph type="italics"/>AbNK.<emph.end type="italics"/> Unde cum &longs;patia in Me&shy;<lb/>dio utroque, in principio de&longs;cen&longs;us vel fine a&longs;cen&longs;us &longs;imul de&longs;crip&shy;<lb/>ta accedunt ad &aelig;qualitatem, adeoque tunc &longs;unt ad invicem ut area <lb/>(<emph type="italics"/>BD<emph.end type="italics"/>XV<emph type="sup"/>2<emph.end type="sup"/>/4<emph type="italics"/>AB<emph.end type="italics"/>) &amp; arearum <emph type="italics"/>DET<emph.end type="italics"/> &amp; <emph type="italics"/>AbNK<emph.end type="italics"/> differentia; ob eorum ana&shy;<lb/>loga incrementa nece&longs;&longs;e e&longs;t ut in &aelig;qualibus quibu&longs;cunque tempo&shy;<lb/>ribus &longs;int ad invicem ut area illa (<emph type="italics"/>BD<emph.end type="italics"/>XV<emph type="sup"/>2<emph.end type="sup"/>/4<emph type="italics"/>AB<emph.end type="italics"/>) &amp; arearum <emph type="italics"/>DET<emph.end type="italics"/> &amp; <lb/><emph type="italics"/>AbNK<emph.end type="italics"/> differentia. <emph type="italics"/><expan abbr="q.">que</expan> E. D.<emph.end type="italics"/></s></p><pb pagenum="253"/><p type="margin"> <s>Nam &longs;patium in Medio non re&longs;i&longs;tente e&longs;t in dupli&shy;<lb/>cata ratione temporis, &longs;ive ut V<emph type="sup"/>2<emph.end type="sup"/>, &amp; ob datas <emph type="italics"/>BD<emph.end type="italics"/> &amp; <emph type="italics"/>AB,<emph.end type="italics"/> ut <pb pagenum="252"/><arrow.to.target n="note228"></arrow.to.target><lb/>(<emph type="italics"/>BD<emph.end type="italics"/>XV<emph type="sup"/>2<emph.end type="sup"/>/4<emph type="italics"/>AB<emph.end type="italics"/>). Momentum hujus are&aelig; &longs;ive huic &aelig;qualis (<emph type="italics"/>DAqXBD<emph.end type="italics"/>XM<emph type="sup"/>2<emph.end type="sup"/>/<emph type="italics"/>DEqXAB<emph.end type="italics"/>) <lb/>e&longs;t ad momentum differenti&aelig; arearum <emph type="italics"/>DET<emph.end type="italics"/> &amp; <emph type="italics"/>AbNK,<emph.end type="italics"/> ut <lb/>(<emph type="italics"/>DAqXBD<emph.end type="italics"/>X2MX<emph type="italics"/>m<emph.end type="italics"/>/<emph type="italics"/>DEqXAB<emph.end type="italics"/>) ad (<emph type="italics"/>APXBDXm/AB<emph.end type="italics"/>), hoc e&longs;t, ut (<emph type="italics"/>DAqXBD<emph.end type="italics"/>XM/<emph type="italics"/>DEq<emph.end type="italics"/>) <lb/>ad 1/2<emph type="italics"/>BDXAP,<emph.end type="italics"/> &longs;ive ut (<emph type="italics"/>DAq/DEq<emph.end type="italics"/>) in <emph type="italics"/>DET<emph.end type="italics"/> ad <emph type="italics"/>DAP<emph.end type="italics"/>; adeoque ubi <lb/>are&aelig; <emph type="italics"/>DET<emph.end type="italics"/> &amp; <emph type="italics"/>DAP<emph.end type="italics"/> quam minim&aelig; &longs;unt, in ratione &aelig;qualitatis. <lb/></s>
  
  <s>&AElig;qualis igitur e&longs;t area quam minima (<emph type="italics"/>BD<emph.end type="italics"/>XV<emph type="sup"/>2<emph.end type="sup"/>/4<emph type="italics"/>AB<emph.end type="italics"/>) differenti&aelig; quam <lb/>minim&aelig; arearum <emph type="italics"/>DET<emph.end type="italics"/> &amp; <emph type="italics"/>AbNK.<emph.end type="italics"/> Unde cum &longs;patia in Me&shy;<lb/>dio utroque, in principio de&longs;cen&longs;us vel fine a&longs;cen&longs;us &longs;imul de&longs;crip&shy;<lb/>ta accedunt ad &aelig;qualitatem, adeoque tunc &longs;unt ad invicem ut area <lb/>(<emph type="italics"/>BD<emph.end type="italics"/>XV<emph type="sup"/>2<emph.end type="sup"/>/4<emph type="italics"/>AB<emph.end type="italics"/>) &amp; arearum <emph type="italics"/>DET<emph.end type="italics"/> &amp; <emph type="italics"/>AbNK<emph.end type="italics"/> differentia; ob eorum ana&shy;<lb/>loga incrementa nece&longs;&longs;e e&longs;t ut in &aelig;qualibus quibu&longs;cunque tempo&shy;<lb/>ribus &longs;int ad invicem ut area illa (<emph type="italics"/>BD<emph.end type="italics"/>XV<emph type="sup"/>2<emph.end type="sup"/>/4<emph type="italics"/>AB<emph.end type="italics"/>) &amp; arearum <emph type="italics"/>DET<emph.end type="italics"/> &amp; <lb/><emph type="italics"/>AbNK<emph.end type="italics"/> differentia. <emph type="italics"/><expan abbr="q.">que</expan> E. D.<emph.end type="italics"/></s></p><pb pagenum="253"/><p type="margin">
  
 <s><margin.target id="note228"></margin.target>DE MOTU <lb/>CORPORUM</s></p><p type="main"> <s><margin.target id="note228"></margin.target>DE MOTU <lb/>CORPORUM</s></p><p type="main">
  
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 <s>id e&longs;t, ita ut &longs;it <emph type="italics"/>AH-BI=b, <lb/>BI-CK=2b, CK-DL=3b, DL+EM=4b,-EM+FN=5b,<emph.end type="italics"/><lb/><figure id="fig241"></figure><lb/>&amp;c. </s> <s>id e&longs;t, ita ut &longs;it <emph type="italics"/>AH-BI=b, <lb/>BI-CK=2b, CK-DL=3b, DL+EM=4b,-EM+FN=5b,<emph.end type="italics"/><lb/><figure id="fig241"></figure><lb/>&amp;c. </s>
  
 <s>dein <emph type="italics"/>b-2b=c,<emph.end type="italics"/> &amp;c. <lb/>&amp; &longs;ic pergatur ad diffe&shy;<lb/>rentiam ultimam qu&aelig; hic <lb/>e&longs;t <emph type="italics"/>f.<emph.end type="italics"/> Deinde erecta qua&shy;<lb/>cunque perpendiculari <lb/><emph type="italics"/>RS,<emph.end type="italics"/> qu&aelig; fuerit ordina&shy;<lb/>tim applicata ad curvam <lb/>qu&aelig;&longs;itam: ut inveniatur <lb/>hujus longitudo, pone <lb/>intervalla <emph type="italics"/>HI, IK, KL, <lb/>LM,<emph.end type="italics"/> &amp;c. </s> <s>dein <emph type="italics"/>b-2b=c,<emph.end type="italics"/> &amp;c. <lb/></s>
  
  <s>&amp; &longs;ic pergatur ad diffe&shy;<lb/>rentiam ultimam qu&aelig; hic <lb/>e&longs;t <emph type="italics"/>f.<emph.end type="italics"/> Deinde erecta qua&shy;<lb/>cunque perpendiculari <lb/><emph type="italics"/>RS,<emph.end type="italics"/> qu&aelig; fuerit ordina&shy;<lb/>tim applicata ad curvam <lb/>qu&aelig;&longs;itam: ut inveniatur <lb/>hujus longitudo, pone <lb/>intervalla <emph type="italics"/>HI, IK, KL, <lb/>LM,<emph.end type="italics"/> &amp;c. </s>
  
 <s>unitates e&longs;&longs;e, <lb/>&amp; dic <emph type="italics"/>AH=a,-HS=p, <lb/>1/2p<emph.end type="italics"/> in -<emph type="italics"/>IS=q, 1/3q<emph.end type="italics"/> in <lb/>+<emph type="italics"/>SK=r, 1/4r<emph.end type="italics"/> in +<emph type="italics"/>SL=s, 1/5s<emph.end type="italics"/> in +<emph type="italics"/>SM=t<emph.end type="italics"/>; pergendo videlicet <lb/>ad u&longs;que penultimum perpendiculum <emph type="italics"/>ME,<emph.end type="italics"/> &amp; pr&aelig;ponendo &longs;igna <lb/>negativa terminis <emph type="italics"/>HS, IS,<emph.end type="italics"/> &amp;c. </s> <s>unitates e&longs;&longs;e, <lb/>&amp; dic <emph type="italics"/>AH=a,-HS=p, <lb/>1/2p<emph.end type="italics"/> in -<emph type="italics"/>IS=q, 1/3q<emph.end type="italics"/> in <lb/>+<emph type="italics"/>SK=r, 1/4r<emph.end type="italics"/> in +<emph type="italics"/>SL=s, 1/5s<emph.end type="italics"/> in +<emph type="italics"/>SM=t<emph.end type="italics"/>; pergendo videlicet <lb/>ad u&longs;que penultimum perpendiculum <emph type="italics"/>ME,<emph.end type="italics"/> &amp; pr&aelig;ponendo &longs;igna <lb/>negativa terminis <emph type="italics"/>HS, IS,<emph.end type="italics"/> &amp;c. </s>
  
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 <s>Inde vero &amp; ex &longs;itu caud&aelig; col&shy;<lb/>ligitur caput fui&longs;&longs;e Soli vicinum. <emph type="italics"/>A Sole,<emph.end type="italics"/> inquit Matth&aelig;us Pari&shy;<lb/>&longs;ien&longs;is, <emph type="italics"/>di&longs;tabat qua&longs;i cubito uno, ab hora tertia<emph.end type="italics"/> [rectius &longs;exta] <emph type="italics"/>u&longs;&shy;<lb/>que ad horam nonam radium ex &longs;e longum emittens.<emph.end type="italics"/> Talis etiam <lb/>erat ardenti&longs;&longs;imus ille Cometa ab <emph type="italics"/>Ari&longs;totele<emph.end type="italics"/> de&longs;criptus Lib. </s> <s>Inde vero &amp; ex &longs;itu caud&aelig; col&shy;<lb/>ligitur caput fui&longs;&longs;e Soli vicinum. <emph type="italics"/>A Sole,<emph.end type="italics"/> inquit Matth&aelig;us Pari&shy;<lb/>&longs;ien&longs;is, <emph type="italics"/>di&longs;tabat qua&longs;i cubito uno, ab hora tertia<emph.end type="italics"/> [rectius &longs;exta] <emph type="italics"/>u&longs;&shy;<lb/>que ad horam nonam radium ex &longs;e longum emittens.<emph.end type="italics"/> Talis etiam <lb/>erat ardenti&longs;&longs;imus ille Cometa ab <emph type="italics"/>Ari&longs;totele<emph.end type="italics"/> de&longs;criptus Lib. </s>
  
 <s>l. <lb/>Meteor. </s> <s>l. <lb/></s>
  
  <s>Meteor. </s>
  
 <s>6. <emph type="italics"/>cujus caput primo die non con&longs;pectum e&longs;t, eo quod ante <lb/>Solem vel &longs;altem &longs;ub radiis &longs;olaribus oceidi&longs;&longs;et, &longs;equente vero die <lb/>quantum potuit vi&longs;um e&longs;t. </s> <s>6. <emph type="italics"/>cujus caput primo die non con&longs;pectum e&longs;t, eo quod ante <lb/>Solem vel &longs;altem &longs;ub radiis &longs;olaribus oceidi&longs;&longs;et, &longs;equente vero die <lb/>quantum potuit vi&longs;um e&longs;t. </s>
  

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